1 Answer

Nickal · Answer 1 · 2023-11-10T02:00:18+0000

Answer:

see attached graphs

Explanation:

Transformations

For a > 0

$f(x+a) \implies f(x) \: \textsf{translated}\:a\:\textsf{units left}$

$f(x-a) \implies f(x) \: \textsf{translated}\:a\:\textsf{units right}$

$f(x)+a \implies f(x) \: \textsf{translated}\:a\:\textsf{units up}$

$f(x)-a \implies f(x) \: \textsf{translated}\:a\:\textsf{units down}$

$y=a\:f(x) \implies f(x) \: \textsf{stretched parallel to the y-axis (vertically) by a factor of}\:a$

$y=f(ax) \implies f(x) \: \textsf{stretched parallel to the x-axis (horizontally) by a factor of} \: (1)/(a)$

$y=-f(x) \implies f(x) \: \textsf{reflected in the} \: x \textsf{-axis}$

$y=f(-x) \implies f(x) \: \textsf{reflected in the} \: y \textsf{-axis}$

Parent function:
f(x) = x

Each transformation is a transformation of the parent function only:

Translation of 4 units down

$\implies f(x)-4=x-4$

$\implies y=x-4$

A stretch by a factor of 3

$\implies 3f(x)=3x$

$\implies y=3x$

A reflection and a translation 1 unit up

$\implies f(-x)+1=-x+1$

$\implies y=-x+1$

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